Combine the macadamia nuts and 1 tablespoon superfine sugar in a food processor. Pulse until finely chopped; pour into a small bowl and set aside. Combine the flour and salt in a medium bowl and set aside.
Beat the butter, remaining 3/4 cup superfine sugar and the lime zest in a large bowl with a mixer on medium-high speed until light and fluffy, 3 to 5 minutes. Beat in the egg until well combined, 1 minute. Reduce the mixer speed to low and beat in the flour mixture. Beat in the food coloring until evenly green. Stir in the macadamia nuts with a rubber spatula.
Turn out the dough onto a large sheet of plastic wrap and shape into a log, about 10 inches long. Wrap tightly and refrigerate until very firm, at least 3 hours or overnight.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Trim the ends of the dough log. Roll the log in green sugar until completely coated. Slice the log into 1/2-inch-thick rounds. Arrange the rounds 2 inches apart on the prepared pans. Sprinkle with more green sugar.
Bake, switching the pans halfway through, until the cookies are firm around the edges but not browned, 17 to 20 minutes. Let cool completely on the pans.